Structural complexity in ramp-compressed sodium to 480 GPa

The properties of all materials at one atmosphere of pressure are controlled by the configurations of their valence electrons. At extreme pressures, neighboring atoms approach so close that core-electron orbitals overlap, and theory predicts the emergence of unusual quantum behavior. We ramp-compress monovalent elemental sodium, a prototypical metal at ambient conditions, to nearly 500 GPa (5 million atmospheres). The 7-fold increase of density brings the interatomic distance to 1.74 Å well within the initial 2.03 Å of the Na+ ionic diameter, and squeezes the valence electrons into the interstitial voids suggesting the formation of an electride phase. The laser-driven compression results in pressure-driven melting and recrystallization in a billionth of a second. In situ x-ray diffraction reveals a series of unexpected phase transitions upon recrystallization, and optical reflectivity measurements show a precipitous decrease throughout the liquid and solid phases, where the liquid is predicted to have electronic localization. These data reveal the presence of a rich, temperature-driven polymorphism where core electron overlap is thought to stabilize the formation of peculiar electride states.

In these experiments, the Omega EP lasers compressed Na to pressures reaching 480 GPa using a shock-ramp compression technique. To prevent the ramp compression wave from steepening into a shock wave, two 10-ns pulses were stitched together to create a 20-ns ramped laser pulse shape with a low-energy "foot" that pre-compresses the Na before the second pulse compresses to the final maximum pressure as shown in SI Figs. 1 and 2. Two beams irradiated the Na sandwich target at an angle of 23 • with respect to the target normal with a peak irradiance of 3.4 ×10 12 W/cm 2 . These drive beams used distributed phase plates that produced a focal spot with a super-Gaussian intensity distribution I = I 0 ×exp − 2 r/550µm 8.0 to ensure transverse spatial uniformity in the sample. Two additional 1250-J beams irradiated a Cu foil with 1-ns square pulses at 2.5 ×10 15 W/cm 2 to create 8.37 keV He-α x-rays for XRD [1]. The x rays are generated over the duration of the pulse length (1-ns) and near the end of the 20-ns main drive.
The experiment uses the Omega EP x-ray diffraction platform, Powder X-ray Diffraction Image Plates (PXRDIP), that is described in Refs. [2,3]. The Debye-Scherrer rings from the compressed Na sample are collected in an image plate (IP) lined box with Kapton (25 µm) and Cu (12.5 -25 µm) filtering to attenuate background x rays other than Cu He-α. IP data analysis involves mapping IP pixels onto the scattering angle, 2θ, according to Ref. [2]. The lattice plane d spacings are calculated using the Bragg condition, λ = 2d sin(θ), for an x-ray wavelength, λ, and x-ray incidence angle, θ. The 2θ resolution for each peak is about 1 degree for a Cu x-ray source (XRS) considering spectral broadening, finite XRS size, and a finite pinhole diameter [3]. In addition to diffraction from Na, calibration diffraction patterns from the edges of a 300µm or 800-µm diameter W or Ta pinhole (75-µm thick) are used to determine the IP, XRS, and pinhole locations relative to the diffraction lines. The larger pinhole diameter is used for the reflectivity measurements to observe the spatial features on the target (Ti stripes). A 300-µm diameter pinhole is used for the XRD-only experiments to reduce the effects of pinhole broadening and transverse pressure gradients.
Because the pinhole diameter (800-µm) is larger than typically used (300-400-µm) and similar to the laser drive spot diameter (1100-µm), the contribution of transverse pressure gradients to the pressure distribution at the time of x-ray exposure is investigated. The transverse-pressure uniformity across the 800-µm line-imaging VISAR field-of-view is evident from the planarity of the fringes as shown in Supplementary Figure 3 (a) for shot 27967. For this shot, the pressure of the cI16 Na sample is 261 ± 11 GPa. For the standard Omega EP PXRDIP geometry as described in Ref. [3] (α = 22.5 • , r x = 24.24 mm), a combined pinhole, sample and window thickness of 100-µm-thick at the time of the x-ray exposure, and an 800-µm-diameter, 75-µm thick Ta pinhole, the impact parameter b is calculated. As shown in Supplementary Figure 3 (b), the impact parameter is the distance away from the aperture axis where b max is the maximum impact parameter visible by any given detector element and b center is the impact parameter for a ray that passes through the center of the pinhole axis to a detector element. The 550-µm (radius of laser drive spot) contours of b center (solid blue) and b max (dashed-blue) are plotted on top of cI16 diffraction data for the same shot. The detector elements to the left of the blue-dashed curve have a b max less than the laser drive spot radius and therefore transverse pressure gradients do not contribute to the pressure histogram in that region. Although b max is larger than the radius of the laser drive spot for the detector elements where two highangle diffraction lines are observed, b center is less than 550-µm at those scattering angles and better describes the majority of the sample volume contributing to the diffraction. The contribution to the pressure distribution from transverse pressure gradients is taken into account by including an asymmetric      d spacing error bar of 0.05Å for the two high angle diffraction peaks because the range of impact parameters will both broaden the diffraction line and contribute a low-pressure tail to the pressure histogram.

A. Pressure determination
The pressure of the Na sample is deduced using data from a line-imaging VISAR [4] that detects Doppler shifts of a 532nm probe beam reflecting off a moving surface in the target (e.g. sample interface through a transparent window or freesurface). The Doppler shifts are manifested as shifts in the fringe pattern recorded in a 2-D interferogram. The fringe shifts are proportional to the changes in the velocity of the reflecting surface and these velocities are used to determine the pressure of the Na samples. The intensity of the VISAR signal provides information about the target reflectance. To see the preimposed striped reflectance pattern more clearly, the etalon leg for one of the interferometers was sometimes blocked to collect a non-fringing image.
The pressure in the Na sample at the time of the x-ray exposure is calculated using hydrodynamics simulations shown in Supplementary The laser power and Na sample thickness are used as free parameters in the hydrodynamics code, HYADES [6], and run iteratively to match the measured interface or free surface velocities by minimizing the χ 2 difference between the measured and simulated velocities. The apparent Na-window interface velocity is first corrected to give the true velocity using the refractive index models for the windows from Refs. [7,8]. The target layers are defined on a mesh of 1300 zones and EOS models for the diamond, Na, and LiF/MgO are SESAME 7834, SESAME 2441, and SESAME 7271v3/SESAME 7460, respectively [9]. The strength of diamond is included using a Steinberg-Guinan model with a shear modulus G 0 80 GPa, yield strength 70 GPa, and pressure-dependence of the shear modulus A 0 = 1/G 0 (dG/dP) = 4.3E-3 GPa −1 [10]. The converged Na sample thickness used in the simulation is within error of the measured Na layer thickness (10%).
The temperature-pressure phase diagram shown in Supplementary Figure 7 shows the data from this work (pink, yellow, and green points). Two error bars are displayed for both the    temperature and pressure. The green, pink, and yellow "error bars" are the standard deviation of the temperature and pressure within the sample at the time of the x-ray probe. The black error bars are the true error bars. The systematic error that dominates the pressure uncertainty is the mechanical response of the diamond, LiF, and MgO windows. For a relatively thin sample and/or long timescale compression (sample and window pressures have equilibrated), the pressure of the Na sample is independent from the sample EOS but does rely on the window EOS. We have confidence in the window EOS, because the LiF and diamond EOS used in the simulations have been benchmarked with experimental results. The ramp EOS of diamond was measured up to 800 GPa where an error of 3% in CL-Up is reported [11] and contributes a 3% error bar for experiments with a diamond window. Uncertainty in diamond strength is estimated by running hydrodynamics simulation with and without a strength model, leading to an asymmetric error in the resulting pressure of at least 50 GPa [12]. A 3% error is introduced in the pressure determination for targets with LiF windows due to the uncertainty in the ramp EOS up to 350 GPa [13]. A 3% error is included for the experiment that used an MgO window due to the uncertainty in the MgO pressuredensity equation-of-state (EOS) measured up to 900 GPa [14]. For LiF and MgO, an additional systematic error of 0.3% and 3%, respectively, is included for the uncertainty in the refractive index correction [7,8]. All experiments include a VISAR phase extraction uncertainty of 5% of the velocity per fringe (VPF) and the VPF's used in the two interferometers were 2.74 and 1.64 µm/ns/fringe.
These experiments rely on hydrocode simulations to estimate the temperatures because there are no temperature measurements. If a shock-ramp path is assumed, then the small initial shock is expected to be similar in all experiments be- The paths are consistent with a weak initial shock in the Na sample (<10 GPa). Our laser-driven ramp compression data are the pink circles, yellow diamond, and green triangles. The data are compared to the theoretical principal Hugoniot (SESAME 2441) and isentrope (LEOS 110). The melting curve data from Refs. [16,17] are shown (blue circles and triangle) along with a Kechin [18] fit to density-functional-theory (DFT) calculations [19] for the melting curve (blue dashed line) above 130 GPa in the hP4 phase. The highest pressure static compression data point from Ref. [20] is shown (gray triangle). cause a 50-J, 10-ns pulse and diamond ablators are used in nearly all experiments as shown in SI Figs. 1 and 2. The hydrodynamics simulation paths for each shot are shown in Supplementary Figure 7 and are consistent with a weak initial shock in the Na sample (< 10GPa). The error bars are given by the average range of temperatures spanned by simulation results within a factor of 2 of the minimum χ 2 difference between the measured and simulated velocities. No systematic errors in the temperature are taken into account. The effects of thermal conduction on the inferred temperature were investigated. The thermal conductivity used in the simulations is Spitzer/Braginski/Lee-More plasma thermal conductivity. The simulations suggest that the layers of the target do not thermalize on the timescales relevant to the experiment (∼20ns) and the heat affected region of the sample is confined to a thin layer adjacent to the window. Simulations with and without the 0.1-µm Ti coating suggest that the Ti does not disturb the hydrodynamics and acts like a reflectance monitor as intended.
The temperature of ramp-compressed Na is inferred from HYADES hydrodynamics simulations and an experimental upper bound is given by streaked optical pyrometry (SOP) measurements [15]. The SOP counts are converted to temperature at the Na-LiF interface following the procedure of Gregor et al.. The Na-LiF interface temperature is inferred using calibration constants A0 = 288,600 ADU/ns, T0 = 1.909 Supplementary Figure 8. Pressure versus density. Pressure versus density for the hP4 phase (green triangles), cI16 (pink circles), and R3m data (yellow diamond) compared to the DFT cold curve in the hP4 phase (dashed-gray curve) [20], pressure-volume data and the H02 relation fit and extrapolation measured by Hanfland et al. up to 100 GPa (blue points and blue curve; extrapolation bluedashed curve) [21], SESAME 2441 principal isentrope (dashed green curve) and Hugoniot (dashed-red curve), LEOS 110 principal isentrope (green curve), and shock hugoniot data from Refs. [22][23][24].
eV, and a Na emissivity, ε = 1-R = 0.77, where R is the Na reflectivity. The reflectivity is constrained by the corresponding VISAR measurements at 532-nm where it was observed to drop to 23%±4% at the x-ray probe time. Based on experimental data on the refractive-index of ramp-compressed LiF to 900, LiF should be transparent at these conditions [7]. The LiF is assumed to be neither absorbing nor emitting over the 590-700 nm diagnostic wavelengths. The experimental data provides an upper bound on the temperature because the LiF is likely to have increasing absorption as the LiF is compressed and heated. This is likely confirmed by the observation that the reference Ti signal is observed to gradually decrease with time.

B. Structure determination
A summary of the data from this work and previous studies in shown in Supplementary Figure 8. The density of the hP4 phase (green triangles), cI16 (pink circles), and R3m data (yellow diamond) are calculated from the XRD data and compared to various theoretical and experimental data [20][21][22][23][24]. IP data and a comparison of the integrated diffraction pattern to the hP4, cI16, and R3m fit are shown in SI Figs. 9, 10, and 11.
To ensure the indexed diffraction peaks are from compressed Na, the diffraction patterns were compared to the expected diffraction patterns from the window materials, LiF and MgO, and the tungsten pinhole. Supplementary Informa- Supplementary Figure 9. hP4 x-ray diffraction pattern. (a) Background subtracted 2θ-φ projections of a Na XRD pattern at 409±15 GPa (shot 25877). (b) The data are compared to the diffraction pattern from the hP4 structure. The reflections from compressed Na are marked with green arrows. The gray shaded regions mark the calibration diffraction peaks.
tion Figure 12 shows a comparison of the diffraction data to the MgO SESAME 7640 and LiF SESAME 7271 v3 isentropes (black curves) and the ambient density tungsten d-spacings (dashed gray lines). Although the diffraction peak observed near 1.8Å is consistent with the LiF (111) line, we believe this peak is from the compressed Na sample because the same peak is observed using an MgO window. In addition, previous experiments using single-crystal LiF as a diagnostic window have not observed a significant change in the LiF texture with compression. The data are also compared to the uncompressed bcc tungsten d-spacings because reference calibration diffraction lines from W are used in these experiments; in some cases, tantalum (bcc) is used instead. Although the reference material is chosen to minimize overlap with the compressed Na diffraction data, the pinhole is responsible the absence of the cI16 (013) peak.   [20], and the SESAME 7460 MgO principal isentrope (black curves). (b) The same data compared to the SESAME 7271 v3 LiF principal isentrope (black curves) and the ambient density tungsten d-spacings (dashed gray lines).